Math Problem Statement

Чему равен определитель от произведения матриц?

Solution

The question in the image is asking:

"Чему равен определитель от произведения матриц?"

This translates to:
"What is the determinant of the product of matrices equal to?"

The answer choices are:

  1. Сумме определителей (Sum of determinants)
  2. Частному определителей (Quotient of determinants)
  3. Произведению определителей (Product of determinants)

Correct Answer:

The determinant of the product of matrices is equal to the product of their determinants.

So, the correct answer is:
"Произведению определителей" (Product of determinants).

Let me know if you'd like a detailed explanation or have any other questions.

Here are some related questions:

  1. What is the formula for the determinant of the inverse of a matrix?
  2. How does the determinant help in solving systems of linear equations?
  3. What happens to the determinant if a matrix is transposed?
  4. What is the determinant of a diagonal matrix?
  5. How can determinants be used to check matrix invertibility?

Tip: The determinant is a useful property to assess whether a matrix is invertible or singular (det = 0 means singular).

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Determinants
Matrices

Formulas

det(AB) = det(A) * det(B)

Theorems

Determinant of matrix product theorem

Suitable Grade Level

Undergraduate (Linear Algebra)